The 32-year-old, who has played twice for Scotland B, was forced to drop out of the squad for their match against Croatia in June with tonsillitis.
Greer hopes that he will be given the opportunity to earn his first cap for the national side in the near future.
"You strive all your life to play for the national team and I was obviously delighted to get called up the first time," Greer told BT Sport.
"We had finished for the season when I got called up for the Croatia game and I was gutted that I couldn't stay due to illness. It is up to me now. It is up to me to train well when I am here, hopefully impress the manager and hopefully get a chance.
"You don't really tinker that much with the back four and the keeper, unless there is an injury or someone gets sent off, so you wait until your chance comes. I am happy to be here and I will train well and hopefully if I continue to do that I will get an opportunity at one point."
Scotland face Croatia in their final World Cup qualifier at Hampden Park on Tuesday evening.